What Is the Tension and Kinetic Friction in This Blocks and Pulleys System?

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In the discussed blocks and pulleys system, three blocks are arranged symmetrically, with two blocks hanging and one on the table. The first block has a mass of M, the second block on the table has a mass of 2M, and the third block also has a mass of 2M. The acceleration is given as 0.5 m/s², and the challenge is to determine the tension in the first string and the kinetic friction of the second block on the table. The equations of motion for each block are set up, but the user struggles with incorporating friction into the calculations. The key to solving the problem lies in correctly adjusting the equation for Block 2 to include the kinetic friction term.
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Three Blocks total, Two on sides hanging off the table, and one Block on table in the middle of the two outer blocks. . . symmetrical.

block1 from left has a mass of M, hanging and connected to a pulley, which is the connected to Block 2(on a table) with Mass of 2M, Block three is also hanging but with mass of 2M. If acceleration is .5m/s^2, What is the Tension on the first string?
what is the Kinetic friction of Black 2 on Table?

Fnet=Ma

I started by writing that Block 3= 2Mg-T2=2Ma
Block 2= T2-T1=2Ma
Block 1= T1-Mg=Ma
I then connected Block3 to Block2, since they share T2
I would add forces but tensions would simply cancel out, at times even masses and Tension, leaving me with known variables=known variables, makes not sense. I tried many ways. This is all the info the book gives, but I feel I'm missing a key idea.


This has been driving me insane.
The tension question was given to me on a test, which I failed answering correctly.
The Kinetic question, I know from back of book, the coefficient of kinetic friction is = .37
But I don't know how exactly how they got to it. Some one please help.
 
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FabricWarp said:
I started by writing that Block 3= 2Mg-T2=2Ma

Good.
Block 2= T2-T1=2Ma

Don't forget that friction acts on Block 2.
Block 1= T1-Mg=Ma

Good.

Correct your equation for Block 2 and you'll be able to solve for the friction, then use that to find μ.
 
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Hi FabricWarp! Welcome to PF! :smile:

(instead of using "SIZE" tags, try using the X2 and X2 tags just above the Reply box :wink:)
FabricWarp said:
Block 2= T2-T1=2Ma


ooh, you're missing the obvious … you need a 2µMg somewhere in there, don't you? :smile:
 
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